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Complete Subgraphs of r-partite Graphs

Published online by Cambridge University Press:  12 September 2008

Guoping Jin
Guoping Jin
Affiliation:
Department of Pure Mathematics and Mathematical Statistics, Cambridge University, England
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Abstract

The smallest minimal degree of an r-partite graph that guarantees the existence of a complete subgraph of order r has been found for the case r = 3 by Bollobás, Erdő and Szemerédi, who also gave bounds for the cases r ≥ 4. In this paper the exact value is established for the cases r = 4 and 5, and the bounds for r ≥ 6 are improved.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 1 , Issue 3 , September 1992 , pp. 241 - 250
Copyright
Copyright © Cambridge University Press 1992

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References

[1]Bollobás, B. (1978) Extremal Graph Theory, Academic Press, London, p. 488.Google Scholar
[2]Bollobás, B., Erdős, P. and Straus, E. C. (1974) Complete subgraphs of chromatic graphs and hypergraphs. Utilitas Math 6 343–347.Google Scholar
[3]Bollobás, B., Erdős, P. and Szemerédi, E. (1974) On complete subgraphs of r-chromatic graphs. Discrete Math 13 97–107.CrossRefGoogle Scholar
[4]Turán, P. (1941) On an extremal problem in graph theory. Mat. Fiz. Lapok 48 436–452. (Hungarian)Google Scholar